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A model for heating the super-hot corona in solar active regions

Nature Astronomy (2024)Cite this article

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Abstract

What physical mechanisms heat the outer solar or stellar atmosphere to million-kelvin temperatures is a fundamental but long-standing open question. In particular, the solar corona in active-region cores contains an even hotter component reaching 10 MK, manifesting as persistent coronal loops in extreme ultraviolet and soft X-ray images, which imposes a stringent energy budget. Here, we present a self-consistent coronal heating model using a state-of-the-art three-dimensional radiative magnetohydrodynamics simulation. We find that the continuous emergence of magnetic flux in active regions keeps driving magnetic reconnections that release energy impulsively but are persistent over time on average. As a result, numerous substructures are heated to 10 MK and then evolve independently. These collectively form the long-lived and stable coronal loops that have been observed. This process provides a heating model that explains the origin of the super-hot coronal plasma and the persistence of hot coronal loops in emerging active regions.

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Fig. 1: 3D model of EUV coronal loops in active-region cores.
Fig. 2: An overview of the evolution of the hot coronal loops in active-region cores.
Fig. 3: 2D slices passing through the current sheet and hot loops at \(t=7.2\,\min\) to illustrate the heating mechanism.
Fig. 4: Temporal evolution of heating quantities.
Fig. 5: Flux emergence in the active region.

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Data availability

The simulation data and analysis tools are available at the Solar Data Center of Nanjing University (https://sdc.nju.edu.cn/d/34ec4acecf294c21be11/)67.

Code availability

We have opted not to make the MURaM code publicly available as it is updated frequently and because running the code needs expert assistance. The numerical methods used in the code are provided in refs. 29,32,58. Interested readers are invited to contact the corresponding authors for more information.

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Acknowledgements

We thank J. H. Guo for help in data processing and Z. F. Li, J. Chen, Y. L. Wang and P. F. Chen for valuable discussions. M.D.D. and F.C. are supported by the National Key R&D Programme of China (Grant Nos. 2021YFA1600504 and 2022YFF0503004) and by the National Natural Science Foundation of China (Grant Nos. 12373054, 12127901 and 12333009). F.C. is also supported by the Programme for Innovative Talents and Entrepreneurs of Jiangsu Province. Z.L. is supported by the Postgraduate Research & Practice Innovation Programme of Jiangsu Province (Grant No. KYCX22_0107). C.W. is supported by the Postgraduate Research & Practice Innovation Programme of Jiangsu Province (Grant No. KYCX23_0118). The simulation data for the analysis are based upon the work supported by the National Center for Atmospheric Research (NCAR), which is a major facility sponsored by the National Science Foundation under Cooperative Agreement No. 1852977. High-performance computing support was provided by Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation.

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Authors and Affiliations

  1. School of Astronomy and Space Science, Nanjing University, Nanjing, China

    Zekun Lu, Feng Chen, M. D. Ding, Can Wang, Yu Dai & Xin Cheng

  2. Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing, China

    Zekun Lu, Feng Chen, M. D. Ding, Can Wang, Yu Dai & Xin Cheng

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  1. Zekun Lu
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Contributions

Z.L. analysed the simulation data. F.C. conceived the study and provided the data. M.D.D. supervised the project. C.W. analysed the observational data. Z.L., F.C. and M.D.D. wrote the manuscript. C.W., Y.D. and X.C. joined discussions and contributed to the revision of the manuscript.

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Correspondence to Feng Chen or M. D. Ding.

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Nature Astronomy thanks Tom Van Doorsselaere, Thomas Williams and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Evolution of the long-lasting hot coronal loops in the cores of the active region NOAA 12242 observed by SDO/AIA.

a, Emission in AIA 94 Å at four snapshots. b, Normalized flux curve in AIA 94 Å integrated within the whole region shown in panel (a). The blue curve represents the 1-8 Å soft X-ray flux observed by the Geostationary Operational Environmental Satellite (GOES). c, Temporal evolution of emission measure (EM) in the region outlined by the red rectangle in panel (a).

Extended Data Fig. 2 Identification of the coronal strand and measurements of its width.

a, A zoom-in view of the synthetic SXR emission in the XRT Al-thick band. b, Distribution of the XRT intensity across the coronal strand. Shown here is the intensity along the red short line in panel (a). The grey dashed line represents the Gaussian fit of the XRT intensity. A constant term is added to the Gaussian function to account for the background intensity. The fitting yields the standard deviation, σ, and the full width at half maximum (FWHM) of the intensity profile. c, Projection of the magnetic field lines along the strand over the SXR emission. The colors of the lines correspond to the colors of seed points in Extended Data Fig. 3b-d, where the red line traces the emission center of the strand. d, Measurement of strand width along the arc length. The width is calculated as twice the mean distance between the central magnetic field line (red) and the edge field lines (white). The grey area shows the range of strand width defined as twice the minimum and maximum distances between the central and edge lines.

Extended Data Fig. 3 Thermodynamic properties of the coronal strand.

a, Synthetic SXR emissivity in the XRT Al-thick band at the y = 45.888 Mm plane. The white box highlights the coronal strand that is identified in Extended Data Fig. 2. b, A zoom-in view of the XRT emissivity. The yellow dashed contour outlines the coronal strand with a temperature of 10.5 MK. The white triangles represent the seed points at the edge of the strand; the red triangle represents the seed point at the emission center of the contoured strand region. c, Number density, ne, of the zoom-in region. d, z-component of the velocity perpendicular to the magnetic field, v⊥z, of the zoom-in region. e, Distribution of temperature along the magnetic field lines integrated through the center seed point (red curve) and edge seed points (grey curves) as denoted in panels (b)–(d). f, Distribution of v⊥z along the center and edge magnetic field lines, with the same notations as in panel (e).

Extended Data Fig. 4 3D modelling of EUV coronal loops in active region cores.

Four snapshots at t=56.0 min (panel a), 2 h 33.2 min (panel b), 3 h 53.4 min (panel c) and 6 h 3.4 min (panel d) are shown. The notations are the same as those of Fig. 1.

Extended Data Fig. 5 2D slices passing through the current sheet and hot loops.

Four snapshots at t = 56.0 min (panel a), 2 h 33.2 min (panel b), 3 h 53.4 min (panel c) and 6 h 3.4 min (panel d) are shown. The notations are the same as those in Fig. 3a,b.

Extended Data Fig. 6 3D contours of the heating rate per particle, Qtot/n, in the active region.

Five snapshots at t = 7.2 min (panel a), 56.0 min (panel b), 2 h 33.2 min (panel c), 3 h 53.4 min (panel d) and 6 h 3.4 min (panel e) are shown. The contour level is 10−17 W. The white solid tubes represent the magnetic fields the same as those in Fig. 1 and Extended Data Fig. 4. The grey slice represents the bottom surface of the domain used for integrating the heating rate in Fig. 4a.

Extended Data Fig. 7 Quantities in the cross section of the hot coronal loops at their feet.

a, 2D distribution of temperature at z = 0.256 Mm. The colored dash-dotted lines outline the ten magnetic field lines passing through the seed points in Extended Data Fig. 8a. b, A zoom-in view of the footpoint region of the loops. The black dashed contour outlines the cross section of the hot loops (log T > 6.5), with an area of 9.55 × 1016cm2. c, Synthetic AIA 94 Å emission at the footpoint region. The colorbar is reversed for better visualization. d, Velocity component vz at the footpoint region. The white dashed line outlines the contour of vz = 150km s−1.

Extended Data Fig. 8 Quantitative distributions of selected physical parameters.

Distributions of temperature (panel a), number density (panel b), z-component of the velocity perpendicular to the magnetic field (panel c), and volumetric heating rate (panel d) are shown. Left panels depict the 2D distributions of the quantities on the cross section of the hot coronal loops at y = 43 Mm. The colored stars mark positions of the seed points of the magnetic field lines on the slice, where the color notations are the same as those in the right panels. The seed points are set evenly along the z-direction in a length of 5 Mm. The field lines passing through these seed points are plotted in Extended Data Fig. 7a. The right panels show distributions of the quantities along the ten field lines.

Extended Data Fig. 9 3D views of the magnetic field lines corresponding to the plasmoid structure.

a, A zoom-in view of the mini flux rope within the current sheet. The viewpoint aligns with that of panel (c), both oriented along the x-direction. The red, green and blue arrows represent x − , y − and z-axes, respectively. b, A zoom-in view from another perspective. c, An overview of the mini flux rope within the current sheet. The colored slice represents the 2D distribution of temperature with the same domain as in Fig. 4e.

Supplementary information

Supplementary Video 1

Temporal evolution of the hot coronal loops in active region cores. Left panels are the synthetic emission in AIA 94 Å. Right panels are the synthetic emission in XRT Al-thick. The notations are the same as those of Fig. 2a.

Supplementary Video 2

Animation for Fig. 3a,b.

Supplementary Video 3

Animation for Fig. 5a–c.

Supplementary Video 4

Animation for Fig. 5d.

Supplementary Video 5

Temporal evolution of the current sheet region at x = 27.648 Mm with a higher temporal resolution. The left panel displays the 2D distribution of temperature. The right panel presents the current density normalized by the magnetic field strength J/B.

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Lu, Z., Chen, F., Ding, M.D. et al. A model for heating the super-hot corona in solar active regions. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02244-5

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